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Simplifying 2x2 + 6x + 4 = 400 Reorder the terms: 4 + 6x + 2x2 = 400 Solving 4 + 6x + 2x2 = 400 Solving for variable 'x'. Reorder the terms: 4 + -400 + 6x + 2x2 = 400 + -400 Combine like terms: 4 + -400 = -396 -396 + 6x + 2x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -396 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-198 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-198 + 3x + x2)' equal to zero and attempt to solve: Simplifying -198 + 3x + x2 = 0 Solving -198 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '198' to each side of the equation. -198 + 3x + 198 + x2 = 0 + 198 Reorder the terms: -198 + 198 + 3x + x2 = 0 + 198 Combine like terms: -198 + 198 = 0 0 + 3x + x2 = 0 + 198 3x + x2 = 0 + 198 Combine like terms: 0 + 198 = 198 3x + x2 = 198 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 198 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 198 + 2.25 Combine like terms: 198 + 2.25 = 200.25 2.25 + 3x + x2 = 200.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + 1.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + 1.5 = 14.150971698 Simplifying x + 1.5 = 14.150971698 Reorder the terms: 1.5 + x = 14.150971698 Solving 1.5 + x = 14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 14.150971698 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 14.150971698 + -1.5 x = 14.150971698 + -1.5 Combine like terms: 14.150971698 + -1.5 = 12.650971698 x = 12.650971698 Simplifying x = 12.650971698Subproblem 2
x + 1.5 = -14.150971698 Simplifying x + 1.5 = -14.150971698 Reorder the terms: 1.5 + x = -14.150971698 Solving 1.5 + x = -14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -14.150971698 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -14.150971698 + -1.5 x = -14.150971698 + -1.5 Combine like terms: -14.150971698 + -1.5 = -15.650971698 x = -15.650971698 Simplifying x = -15.650971698Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.650971698, -15.650971698}Solution
x = {12.650971698, -15.650971698}
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